Advancements in disciplines ranging from atomic physics to various branches of condensed matter physics are being employed to fabricate a variety of different diamond-based materials that can be used in many different technological applications. Diamond has a crystal lattice structure comprising two interpenetrating face-centered cubic lattices of carbon atoms. FIG. 1A shows a unit cell 100 of a diamond-crystal lattice. In FIG. 1A, each carbon atom, represented by a sphere, is covalently bonded to four adjacent carbon atoms, each covalent bond is represented by a rod connecting two spheres. As shown in FIG. 1A, a carbon atom 102 is covalently bonded to four carbon atoms 103-106. In general, diamond has a number of potentially useful properties. For example, diamond is transparent from the ultraviolet to the far infrared of the electromagnetic spectrum and has a relatively high refractive index of about 2.42. Diamond may also be a suitable replacement for silicon in silicon-based semiconductor devices. For example, silicon has an electronic bandgap of about 1.12 eV and starts to show signs of thermal stress at about 100° C., while diamond has a larger electronic bandgap ranging from about 5 eV to about 7 eV and a higher Debye temperature ranging from about 1550° C. to about 1930° C.
Certain impurities and defects, called “color centers,” embedded in diamond may have potential applications in quantum computing and quantum information processing. For example, a nitrogen-vacancy (“NV”) center embedded in diamond is a type of color center that may be used to store a quantum bit of information. FIG. 1B shows an NV center embedded in a diamond-crystal lattice 110. The NV-center comprises a nitrogen atom 112, substituted for a carbon atom, next to a vacancy 114 in the carbon lattice. The nitrogen atom 112 is covalently bonded to three carbon atoms 116-118. NV centers can be created in a nitrogen rich diamond by irradiation and subsequent annealing at temperatures above 550° C. The radiation creates vacancies in the diamond and subsequent annealing causes the vacancies to migrate towards nitrogen atoms to produce NV centers. Alternatively, NV centers can be created in diamond using N+ ion implantation.
When an electromagnetic field interacts with an NV center, there is a periodic exchange, or oscillation, of energy between the electromagnetic field and the electronic energy levels of the NV center. Such oscillations, which are called “Rabi oscillations,” are associated with oscillations of the NV center electronic energy level populations and quantum-mechanical probability amplitudes of the NV center electronic energy states. Rabi oscillations can be interpreted as an oscillation between absorption and stimulated emission of photons. The Rabi frequency, denoted by Ω, represents the number of times these oscillations occur per unit time (multiplied by the quantity 2π).
FIG. 1C illustrates an energy-level diagram of electronic states of a negatively charged NV center. Under applied stress or an electric field, the E3 excited states, which have an optical doublet, spin striplet structure, split into upper and lower branches with different orbital states. Only the lower branch of the excited states, consisting of three spin levels, is shown in the FIG. 1C. Normally, the optical transitions are normally spin converging. However, when the orbital splitting induced by the applied stress or electric field is in a range from about 15 GHz to about 45 GHz, the spin-orbit interaction can mix the excited states so that spin-non-conserving transitions become allowed In this case, it may be possible to obtain A-type configuration comprising multiple ground states coupled to a common excited state. The three ground 3A2 states comprise a first ground state |1 with a lowest energy level 122, and a pair of nearly degenerate ground states |2 and |3 with energy levels 124 and 126, respectively. In FIG. 1C, all three ground states are coupled to an excited state 128, labeled |4. The three double-headed directional arrows 130-132, corresponds to optical transitions driven by two laser frequencies. A first laser drives the |1→|4 transition, while a second laser drives both the |2→|4 and the |3→|4 transitions. A parameter δ1 represents the laser frequency detuning for a |1→|4 transition, a parameter δ2 is the laser frequency detuning for a |2→|4 transition, a parameter δ23 is the |2⇄|3 energy splitting, and Ωi represent Rabi frequencies, which are proportional to the square root of the laser intensities. When δ1=δ2 or δ1=δ2+δ3, the system will relax through spontaneous emission into stable “dark” states, which are linear combinations of the states |1, |2, and |3, with probability amplitudes that are tunable through the laser amplitudes. These dark resonance states can be used, for example, for all-optical manipulation of the electron spin. For a description of experimental investigations of NV centers, see “The nitrogen-vacancy center in diamond re-visted,” by N. B. Manson et al., preprint: http://arxiv.org/abs/cond-mat/0601360; “Coherent population trapping with a single spin in diamond,” by Charles Santori et al., preprint: http://arxiv.org/abs/quant-ph/0607147; and “Coherent population trapping in Diamond N-V centers at zero magnetic field,” by Charles Santori et al., preprint: http://arxiv.org/abs/cond-mat/0602573. Note that the exact structure of the 3E state depends on the strain or other mechanical effects exterted on the diamond crystal. Also, the excited-state linewidths depend critically on the temperature. In order to obtain optical linewidths that are less than 100 MHz, it is necessary to lower the temperature of the diamond crystal to temperatures below 20K. With narrow optical linewidths, it is possible to manipulate the spins of single NV centers using the optical transitions shown in FIG. 1C.
The NV centers are appealing for quantum information processing because the NV center has a relatively long-lived spin coherence time and a possibility of large-scale integration into semiconductor processing technology. For example, an NV center electron spin coherence time of 58 μs has been observed at room temperature. See “Long coherence times at 300K for nitrogen-vacancy center spins in diamond grown by chemical vapor deposition,” by A. Kennedy et al., App. Phys. Lett. 83, 4190-4192 (2003). NV centers may have relatively long-lived spin coherence because the lattice comprises primarily 12C, which has zero nuclear spin. In addition, a single photon can be generated from an NV center at room temperature, which has established NV centers as potential photon sources for quantum cryptography. See “Stable solid-state source of single photons,” by C. Kurtsiefer et al., Phys. Rev. Lett. 85, 290-293 (2000) and “Room temperature stable single photon source,” by A. Beveratos et al., Eur. Phys. J. D 18, 191-196 (2002).
However, in order to fully realize the potential of diamond color centers for photonic quantum information processing it is necessary to optically couple the diamond color centers to photonic devices, such as resonant cavities and waveguides, which can be used to transmit quantum information encoded in modes of electromagnetic radiation. The photonic devices can be formed in semiconductor materials and used as components of quantum computer architectures. When the coupling between the color center and the cavity or waveguide is sufficiently strong, efficient inter-conversion between photonic and spin qubits becomes possible. One can then envision connecting many such devices together by employing optical waveguides to realize a scalable quantum computing architecture. Physicists, computer scientists, and engineers have, therefore, recognized a need for methods of optically coupling diamond with photonic devices in order to fabricate various quantum computing architectures.